Static output feedback simultaneous stabilization: ILMI approach

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Abstract
In this note, the static output feedback simultaneous stabilization problem is addressed using a matrix inequality approach. A necessary and sufficient condition for simultaneous stabilizability of r proper MIMO plants via static output feedback is obtained. It is proven that the existence of a stabilizing feedback gain which simultaneously stabilizes this set of plants is equivalent to that of the solution of a set of coupled quadratic matrix inequalities. An iterative LMI (ILMI) algorithm based on the linear matrix inequality technique is proposed to obtain the feedback gain. Illustrated examples show its effectiveness.

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